Finite Group Databasebeta

← C3×#63922 #11723247

Subgroups — C3×#63922 #11723247

Order 864.

658 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 658 conjugacy classes of subgroups — too many to draw. Only its 108 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×D32C211yesmaximal, characteristic, complemented
2C2×C32×D12C211yesmaximal, characteristic, complemented
3C2×C3×#626C211yesmaximal, characteristic, complemented
4C2×C3×#625C211yesmaximal, characteristic, complemented
5C3×#3752C211yesmaximal, characteristic, complemented
6C32×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
7C3×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
8C3×#937—31nomaximal
9C3×#882—31nomaximal
10#63922C311yesmaximal, characteristic, direct product factor
11C22×C3×C3⋊D3C2211yescharacteristic
12C22×C32×D3C2211yescharacteristic
13C22×C32×D3C2211yescharacteristic
14C22×C32×D3C2211yescharacteristic, complemented
15C2×C3×D32—22no—
16C2×C3×D32—22no—
17C2×C3×D32—22no—
18C2×C33×C4C2211yescharacteristic, complemented
19C2×C3×C3⋊Dic3C2211yescharacteristic, complemented
20C2×C32×Dic3C2211yescharacteristic, complemented
21C32×D12—22no—
22C3×#626—22no—
23C3×#625—22no—
24C23×C3×D3—31no—
25C23×C3×D3—31no—
26C22×D32C2×C311yescharacteristic, complemented
27C2×C32×D4—31no—
28C2×C3×#67—31no—
29C2×C3×#67—31no—
30C2×C3×#67—31no—
31C2×C3×D12—21no—
32C2×C3×D12—31no—
33C2×C3×D12D311yescharacteristic, complemented
34C2×C3×D12C2×C311yescharacteristic, complemented
35C2×#626C2×C311yescharacteristic, complemented
36C2×#625C2×C311yescharacteristic, complemented
37C32×C22⋊C4—31no—
38#3752C2×C311yescharacteristic, complemented
39C3×#217—31no—
40C3×(C2×D3)⋊C4—21no—
41C3×(C2×D3)⋊C4—31no—
42C3×(C2×D3)⋊C4—31no—
43C3×(C2×D3)⋊C4—31no—
44C3×(C2×D3)⋊C4—61no—
45C3×(C2×D3)⋊C4D311yescharacteristic, complemented
46C3×(C2×D3)⋊C4C2×C311yescharacteristic, complemented
47(C2×D3)⋊Dic3C2×C311yescharacteristic, complemented
48C22×C33C2311yescharacteristic
49C2×C3×C3⋊D3—21no—
50C2×C3×C3⋊D3—21no—
51C2×C3×C3⋊D3D412yescomplemented
52C2×C32×D3—21no—
53C2×C32×D3—21no—
54C2×C32×D3—21no—
55C2×C32×D3—21no—
56C2×C32×D3—21no—
57C2×C32×D3—21no—
58C2×C32×D3—21no—
59C2×C32×D3D412yescomplemented
60C2×C32×D3D412yescomplemented
61C3×D32—28no—
62C33×C4—21no—
63C3×C3⋊Dic3—21no—
64C32×Dic3—21no—
65C3×#120—91no—
66#937—31no—
67#882—31no—
68C23×C32—31no—
69C23×C32—31no—
70C23×C32—31no—
71C22×C3⋊D3C22×C311yescharacteristic
72C22×C3×D3—21no—
73C22×C3×D3—21no—
74C22×C3×D3—21no—
75C22×C3×D3—31no—
76C22×C3×D3—31no—
77C22×C3×D3—61no—
78C22×C3×D3—62no—
79C22×C3×D3—62no—
80C22×C3×D3—62no—
81C22×C3×D3—62no—
82C22×C3×D3—62no—
83C22×C3×D3—62no—
84C22×C3×D3C2×D311yescharacteristic
85C22×C3×D3C2×D311yescharacteristic
86C22×C3×D3C2×D311yescharacteristic, complemented
87C22×C3×D3C22×C311yescharacteristic
88C22×C3×D3C22×C311yescharacteristic
89C22×C3×D3C22×C311yescharacteristic, complemented
90C2×D32—22no—
91C2×D32—22no—
92C2×D32—22no—
93C32×D4—62no—
94C2×C32×C4—21no—
95C2×C32×C4—21no—
96C2×C32×C4—21no—
97C2×C32×C4—31no—
98C2×C32×C4—41no—
99C2×C32×C4C2×D311yescharacteristic, complemented
100C2×C32×C4C2×D311yescharacteristic, complemented
101C2×C32×C4C22×C311yescharacteristic, complemented
102C2×C3⋊Dic3C22×C311yescharacteristic, complemented
103C3×#67—62no—
104C3×#67—62no—
105C3×#67—62no—
106C2×C3×Dic3—21no—
107C2×C3×Dic3—31no—
108C2×C3×Dic3—31no—
109C2×C3×Dic3—61no—
110C2×C3×Dic3C2×D311yescharacteristic, complemented
111C2×C3×Dic3C22×C311yescharacteristic, complemented
112C3×D12—24no—
113C3×D12—22no—
114C3×D12—22no—
115C3×D12—62no—
116#626—22no—
117#625—22no—
118C2×C33C2×D411yescharacteristic
119C2×C33C2×D411yescharacteristic
120C2×C33C2×D411yescharacteristic
121C3×C3⋊D3—22no—
122C32×D3—22no—
123C32×D3—22no—
124C32×D3—41no—
125C24×C3—91no—
126C23×D3—31no—
127C23×D3—31no—
128C2×C3×D4—31no—
129C2×C3×D4—31no—
130C2×C3×D4—61no—
131C2×C3×D4—91no—
132C2×C3×D4—91no—
133C2×#67—31no—
134C2×#67—31no—
135C2×#67—31no—
136C2×D12—31no—
137C2×D12C3×D311yescharacteristic, complemented
138C3×C22⋊C4—31no—
139C3×C22⋊C4—31no—
140C3×C22⋊C4—61no—
141C3×C22⋊C4—91no—
142C3×C22⋊C4—91no—
143#217—31no—
144(C2×D3)⋊C4—31no—
145(C2×D3)⋊C4—31no—
146(C2×D3)⋊C4—31no—
147(C2×D3)⋊C4—61no—
148(C2×D3)⋊C4C3×D311yescharacteristic, complemented
149C22×C32—21no—
150C22×C32—21no—
151C22×C32—21no—
152C22×C32—32no—
153C22×C32—32no—
154C22×C32—41no—
155C22×C32—61no—
156C22×C32—61no—
157C22×C32—61no—
158C22×C32—61no—
159C22×C32—61no—
160C22×C32—61no—
161C22×C32—61no—
162C22×C32C22×D311yescharacteristic
163C22×C32C22×D311yescharacteristic
164C22×C32C23×C311yescharacteristic
165C2×C3⋊D3—21no—
166C2×C3⋊D3—21no—
167C2×C3⋊D3C3×D412yescomplemented
168C2×C3×D3—21no—
169C2×C3×D3—21no—
170C2×C3×D3—21no—
171C2×C3×D3—21no—
172C2×C3×D3—21no—
173C2×C3×D3—21no—
174C2×C3×D3—21no—
175C2×C3×D3—21no—
176C2×C3×D3—22no—
177C2×C3×D3—21no—
178C2×C3×D3—21no—
179C2×C3×D3—21no—
180C2×C3×D3—21no—
181C2×C3×D3—21no—
182C2×C3×D3—21no—
183C2×C3×D3—22no—
184C2×C3×D3—22no—
185C2×C3×D3—32no—
186C2×C3×D3—32no—
187C2×C3×D3—41no—
188C2×C3×D3—41no—
189C2×C3×D3—41no—
190C2×C3×D3—41no—
191C2×C3×D3—41no—
192C2×C3×D3—41no—
193C2×C3×D3—62no—
194C2×C3×D3—68no—
195C2×C3×D3—68no—
196C2×C3×D3—61no—
197C2×C3×D3—61no—
198C2×C3×D3—61no—
199C2×C3×D3—61no—
200C2×C3×D3—121no—
201C2×C3×D3—121no—
202C2×C3×D3D1212yescomplemented
203C2×C3×D3#6712yescomplemented
204C2×C3×D3C3×D412yescomplemented
205C2×C3×D3C3×D412yescomplemented
206D32—28no—
207C32×C4—21no—
208C32×C4—22no—
209C32×C4—21no—
210C32×C4—21no—
211C32×C4—41no—
212C32×C4—41no—
213C32×C4—42no—
214C32×C4—61no—
215C3⋊Dic3—21no—
216C3×Dic3—21no—
217C3×Dic3—21no—
218C3×Dic3—41no—
219C3×Dic3—61no—
220C3×Dic3—61no—
221C3×Dic3—121no—
222#120—91noSylow
223C33#12011yescharacteristic, complemented, Sylow
224C23×C3—31no—
225C23×C3—31no—
226C23×C3—31no—
227C23×C3—31no—
228C23×C3—31no—
229C23×C3—31no—
230C23×C3—61no—
231C23×C3—61no—
232C23×C3—61no—
233C23×C3—91no—
234C23×C3—182no—
235C23×C3—182no—
236C23×C3—182no—
237C22×D3—31no—
238C22×D3—31no—
239C22×D3—61no—
240C22×D3—62no—
241C22×D3—62no—
242C22×D3—62no—
243C22×D3—62no—
244C22×D3—62no—
245C22×D3—62no—
246C22×D3C2×C3×D311yescharacteristic
247C22×D3C2×C3×D311yescharacteristic
248C22×D3C2×C3×D311yescharacteristic, complemented
249C3×D4—62no—
250C3×D4—62no—
251C3×D4—64no—
252C3×D4—182no—
253C3×D4—182no—
254C2×C3×C4—21no—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4—31no—
258C2×C3×C4—31no—
259C2×C3×C4—41no—
260C2×C3×C4—61no—
261C2×C3×C4—91no—
262C2×C3×C4D3211yescharacteristic, complemented
263C2×C3×C4C2×C3×D311yescharacteristic, complemented
264C2×C3×C4C2×C3×D311yescharacteristic, complemented
265#67—62no—
266#67—62no—
267#67—62no—
268C2×Dic3—31no—
269C2×Dic3—31no—
270C2×Dic3—61no—
271C2×Dic3C2×C3×D311yescharacteristic, complemented
272D12—22no—
273D12—62no—
274C2×C32—21no—
275C2×C32—21no—
276C2×C32—21no—
277C2×C32—21no—
278C2×C32—21no—
279C2×C32—21no—
280C2×C32—21no—
281C2×C32—21no—
282C2×C32—21no—
283C2×C32—41no—
284C2×C32—41no—
285C2×C32—41no—
286C2×C32—62no—
287C2×C32—62no—
288C2×C32—121no—
289C2×C32C2×D1211yescharacteristic
290C2×C32D3×D411yescharacteristic
291C2×C32D3×D411yescharacteristic
292C2×C32D3×D411yescharacteristic
293C2×C32D3×D411yescharacteristic
294C2×C32C2×#6711yescharacteristic
295C2×C32C2×C3×D411yescharacteristic
296C2×C32C2×C3×D411yescharacteristic
297C2×C32C2×C3×D411yescharacteristic
298C3⋊D3—22no—
299C3×D3—22no—
300C3×D3—22no—
301C3×D3—22no—
302C3×D3—22no—
303C3×D3—42no—
304C3×D3—42no—
305C3×D3—42no—
306C3×D3—41no—
307C3×D3—41no—
308C3×D3—62no—
309C3×D3—62no—
310C3×D3—122no—
311C24—91no—
312C2×D4—31no—
313C2×D4—91no—
314C2×D4—91no—
315C22⋊C4—31no—
316C22⋊C4—91no—
317C22⋊C4—91no—
318C22×C3—21no—
319C22×C3—21no—
320C22×C3—21no—
321C22×C3—32no—
322C22×C3—32no—
323C22×C3—32no—
324C22×C3—32no—
325C22×C3—41no—
326C22×C3—62no—
327C22×C3—62no—
328C22×C3—62no—
329C22×C3—61no—
330C22×C3—61no—
331C22×C3—61no—
332C22×C3—61no—
333C22×C3—61no—
334C22×C3—61no—
335C22×C3—61no—
336C22×C3—61no—
337C22×C3—61no—
338C22×C3—61no—
339C22×C3—61no—
340C22×C3—61no—
341C22×C3—61no—
342C22×C3—61no—
343C22×C3—92no—
344C22×C3—121no—
345C22×C3—121no—
346C22×C3—121no—
347C22×C3—121no—
348C22×C3—121no—
349C22×C3—121no—
350C22×C3—188no—
351C22×C3—181no—
352C22×C3—181no—
353C22×C3C2×D3211yescharacteristic
354C22×C3C22×C3×D311yescharacteristic
355C22×C3C22×C3×D311yescharacteristic
356C2×D3—21no—
357C2×D3—21no—
358C2×D3—21no—
359C2×D3—21no—
360C2×D3—21no—
361C2×D3—21no—
362C2×D3—21no—
363C2×D3—32no—
364C2×D3—32no—
365C2×D3—62no—
366C2×D3—68no—
367C2×D3—68no—
368C2×D3—61no—
369C2×D3—61no—
370C2×D3—61no—
371C2×D3—61no—
372C2×D3—121no—
373C2×D3—121no—
374C2×D3C3×D1212yescomplemented
375C2×D3C3×#6712yescomplemented
376C3×C4—22no—
377C3×C4—21no—
378C3×C4—21no—
379C3×C4—21no—
380C3×C4—41no—
381C3×C4—41no—
382C3×C4—42no—
383C3×C4—61no—
384C3×C4—61no—
385C3×C4—121no—
386C3×C4—181no—
387Dic3—21no—
388Dic3—61no—
389Dic3—61no—
390Dic3—121no—
391C32—21no—
392C32—21no—
393C32—21no—
394C32—41no—
395C32#88211yescharacteristic, complemented
396C32#93711yescharacteristic, complemented
397C32C3×#12011yescharacteristic, complemented
398C23—31no—
399C23—31no—
400C23—31no—
401C23—91no—
402C23—182no—
403C23—182no—
404C23—182no—
405D4—62no—
406D4—182no—
407D4—182no—
408C2×C4—31no—
409C2×C4—91no—
410C2×C4C3×D3211yescharacteristic, complemented
411C2×C3—21no—
412C2×C3—21no—
413C2×C3—21no—
414C2×C3—21no—
415C2×C3—21no—
416C2×C3—21no—
417C2×C3—21no—
418C2×C3—21no—
419C2×C3—21no—
420C2×C3—41no—
421C2×C3—41no—
422C2×C3—41no—
423C2×C3—62no—
424C2×C3—62no—
425C2×C3—62no—
426C2×C3—62no—
427C2×C3—122no—
428C2×C3—122no—
429C2×C3—122no—
430C2×C3—121no—
431C2×C3—121no—
432C2×C3—182no—
433C2×C3D3×D1211yescharacteristic
434C2×C3#380211yescharacteristic
435C2×C3D3×#6711yescharacteristic
436C2×C3C2×C3×D1211yescharacteristic
437C2×C3C3×D3×D411yescharacteristic
438C2×C3C3×D3×D411yescharacteristic
439C2×C3C3×D3×D411yescharacteristic
440C2×C3C3×D3×D411yescharacteristic
441C2×C3C2×C3×#6711yescharacteristic
442D3—22no—
443D3—22no—
444D3—41no—
445D3—62no—
446D3—62no—
447D3—122no—
448C22—32no—
449C22—32no—
450C22—61no—
451C22—61no—
452C22—61no—
453C22—61no—
454C22—61no—
455C22—61no—
456C22—61no—
457C22—92no—
458C22—188no—
459C22—181no—
460C22—181no—
461C22C2×C3×D3211yescharacteristic
462C4—21no—
463C4—61no—
464C4—181no—
465C3—21no—
466C3—21no—
467C3—21no—
468C3—41no—
469C3#6392211yescharacteristic, direct product factor
470C3C3×#88211yescharacteristic, complemented
471C3C3×#93711yescharacteristic, complemented
472C2—62no—
473C2—62no—
474C2—121no—
475C2—182no—
476C2C3×D3×D1211yescharacteristic
477C2C3×#380211yescharacteristic
478C2C3×D3×#6711yescharacteristic
subgroupG/H
centerC22×C3C2×D32
commutator, cosocleC22×C32C23×C3
FrattiniC22C2×C3×D32
FittingC2×C33×C4C22
socleC22×C33C23
hypercenterC2×C3×C4D32
hypocenterC32C3×#120
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C2×C3×C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C22×C3×D32C2semidirect
2. C2×C32×D12C2semidirect
3. C2×C3×#626C2semidirect
4. C2×C3×#625C2semidirect
5. C3×#3752C2semidirect
6. C32×(C2×D3)⋊C4C2semidirect
7. C3×(C2×D3)⋊Dic3C2semidirect
10. #63922C3direct (N × H)
14. C22×C32×D3C22semidirect
18. C2×C33×C4C22semidirect
19. C2×C3×C3⋊Dic3C22semidirect
20. C2×C32×Dic3C22semidirect
26. C22×D32C2×C3semidirect
33. C2×C3×D12D3semidirect
34. C2×C3×D12C2×C3semidirect
35. C2×#626C2×C3semidirect
36. C2×#625C2×C3semidirect
38. #3752C2×C3semidirect
45. C3×(C2×D3)⋊C4D3semidirect
46. C3×(C2×D3)⋊C4C2×C3semidirect
47. (C2×D3)⋊Dic3C2×C3semidirect
51. C2×C3×C3⋊D3D4semidirect
59. C2×C32×D3D4semidirect
60. C2×C32×D3D4semidirect
86. C22×C3×D3C2×D3semidirect
89. C22×C3×D3C22×C3semidirect
99. C2×C32×C4C2×D3semidirect
100. C2×C32×C4C2×D3semidirect
101. C2×C32×C4C22×C3semidirect
102. C2×C3⋊Dic3C22×C3semidirect
110. C2×C3×Dic3C2×D3semidirect
111. C2×C3×Dic3C22×C3semidirect
137. C2×D12C3×D3semidirect
148. (C2×D3)⋊C4C3×D3semidirect
167. C2×C3⋊D3C3×D4semidirect
202. C2×C3×D3D12semidirect
203. C2×C3×D3#67semidirect
204. C2×C3×D3C3×D4semidirect
205. C2×C3×D3C3×D4semidirect
223. C33#120semidirect
248. C22×D3C2×C3×D3semidirect
262. C2×C3×C4D32semidirect
263. C2×C3×C4C2×C3×D3semidirect
264. C2×C3×C4C2×C3×D3semidirect
271. C2×Dic3C2×C3×D3semidirect
374. C2×D3C3×D12semidirect
375. C2×D3C3×#67semidirect
395. C32#882semidirect
396. C32#937semidirect
397. C32C3×#120semidirect
410. C2×C4C3×D32semidirect
469. C3#63922direct (N × H)
470. C3C3×#882semidirect
471. C3C3×#937semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×C3×D322
C2×C32×D122
C2×C3×#6262
C2×C3×#6252
C3×#37522
C32×(C2×D3)⋊C42
C3×(C2×D3)⋊Dic32
C3×#9373
C3×#8823
#639223